Random hypothesis generation is central to robust geometric model fitting in computer vision. The predominant technique is to randomly sample minimal or elemental subsets of the data, and hypothesize the geometric model from the selected subsets. While taking minimal subsets increases the chance of simultaneously “hitting” inliers in a sample, it amplifies the noise of the underlying model, and hypotheses fitted on minimal subsets may be severely biased even if they contain purely inliers. In this paper we propose to use Random Cluster Models, a technique used to simulate coupled spin systems, to conduct hypothesis generation using subsets larger than minimal. We show how large clusters of data from genuine instances of the geometric model can be efficiently harvested to produce more accurate hypotheses. To take advantage of our hypothesis generator, we construct a simple annealing method based on graph cuts to fit multiple instances of the geometric model in the data. Experimental results show clear improvements in efficiency over other methods based on minimal subset samplers.